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-sets of reals

  • Haim Judah (a1) (a2) (a3) (a4) and Saharon Shelah (a1) (a2) (a3) (a4)

Abstract

We build models where all -sets of reals are measurable and (or) have the property of Baire and (or) are Ramsey. We will show that there is no implication between any of these properties for -sets of reals.

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References

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[BA]Baumgartner, J., Iterated forcing, Surveys of set theory, London Mathematical Society Lecture Note Series, no. 87, Cambridge University Press, 1983.
[HS]Harrington, L. and Shelah, S., Some exact equiconsistency results in set theory, Notre Dame Journal of Formal Logic, vol. 26 (1985).
[JU1]Judah, H., -sets of reals, this Journal, vol. 53 (1988), pp. 636642.
[JU2]Judah, H., Exact consistency results for -sets of reals, preprint.
[JS]Judah, H. and Shelah, S., Martin's axioms, measurability and equiconsistency results, this Journal, vol. 54 (1989), pp. 7894.
[JS1]Judah, H. and Shelah, S., Souslin forcing, this Journal, vol. 53 (1988), pp. 11881207.
[JS2]Judah, H. and Shelah, S., Δ21-sets of reals, Annals of Pure and Applied Logic, vol. 42 (1989).
[JE]Jech, T., Set theory, Academic Press, San Diego, CA.
[RS]Raisonnier, J. and Stern, J., The strength of measurability hypotheses, Israel Journal of Mathematics, vol. 50(1985).
[SH]Shelah, S., Proper forcing, Lectures Notes in Mathematics, vol. 940, Springer-Verlag, Berlin and New York.
[SHI]Shelah, S., Can you take Solovay's inaccesible away?, Israel Journal of Mathematics, vol. 48 (1984).
[SO]Solovay, R. M., A model of set theory in which every set of reals is Lebesgue measurable. Annals of Mathematics, 1970.
[ST1]Stern, J., Generic extensions which do not add random reals. Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, Berlin and New York, 1985.
[ST2]Stern, J., Regularity properties of definable set of reals, Annals of Pure and Applied Logic, vol. 29 (1985).
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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